Question

The sides of an equilateral triangle are x+y-1 , 2x-3y+1 and 3x-y-9 then the values of x and y are

Answer 1

Answer:

$\sf{The \ value \ of \ x \ is \ 6 \ and \ the \ value \ of}$

$\sf{y \ is \ 2.}$

Given:

• Sides of equilateral triangle are:

• x+y-1

• 2x-3y+1

• 3x-y-9

To find:

• The values of x and y.

Solution:

$\sf{Sides \ of \ equilateral \ triangle \ are \ congruent}$

$\sf{\therefore{x+y-1=2x-3y+1}}$

$\sf{\therefore{2x-x-3y-y=-2}}$

$\sf{\therefore{x-4y=-2...(1)}}$

$\sf{Also,}$

$\sf{x+y-1=3x-y-9}$

$\sf{\therefore{3x-x-y-y=8}}$

$\sf{\therefore{2x-2y=8}}$

$\sf{\therefore{2(x-y)=8}}$

$\sf{\therefore{x-y=\dfrac{8}{2}}}$

$\sf{\therefore{x-y=4...(2)}}$

$\sf{Subtract \ equation(1) \ from \ equation(2), \ we \ get}$

$\sf{x-y=4}$

$\sf{-}$

$\sf{x-4y=-2}$

__________________

$\sf{3y=6}$

$\sf{\therefore{y=\dfrac{6}{3}}}$

$\boxed{\sf{\therefore{y=2}}}$

$\sf{Substitute \ y=2 \ in \ equation(2), \ we \ get}$

$\sf{x-2=4}$

$\sf{\therefore{x=4+2}}$

$\boxed{\sf{\therefore{x=6}}}$

$\sf\purple{\tt{\therefore{The \ value \ of \ x \ is \ 6 \ and \ the \ value \ of}}}$

$\sf\purple{\tt{y \ is \ 2.}}$